J. Phys. Chem. 1993,97, 10059-10063
10059
Effect of Stirring and Temperature on the Belousov-Zhabotinskii Reaction in a CSTR A. K. Dutt' and S . C. Miiller Max-Planck-Institut fur Molekulare Physiologie, Rheinlanddamm 201, W4600 Dortmund 1. Germany Received: June 1 I , 19930 The effect of stirring and temperature on the BZ reaction is reported by using malonic and gallic acid as organic substrates in experiments carried out in a continuously fed stirred tank reactor. Complex oscillations of varying frequencies and amplitudes are reported for the gallic acid system at low flow and stirring rate. High temperature decreases the oscillation amplitude in both systems. The oscillation amplitude increases with increase of stirring rate in the gallic acid system, but no significant stirring effect is observed in the malonic acid system for the concentration of the chemicals used. A bistability between an oscillatory branch and a flow branch is reported for the first time for the GA system by using the stirring rate as the control parameter. This indicates the complex dynamical role of temperature and stirring rate as bifurcation parameters in Hopf bifurcation experiments.
Introduction The effect of stirring' in nonlinear chemicalsystem has become a subject of growing interest for the recent few years. Stirring effect is expected to be observed in a chemical system if the mixing time is slow compared to the time scale of the chemical processes. Most studies in the past on the effects of oxygen and stirring on the Belousov-Zhabotinskii (BZ) reaction have been carried out in a batch reactor and the results reported by different groups about oxygen effect were sometimes found to contradict& one another. Recently Lopez-Thomas et a1.2bobserved that if a bromide-selective electrode is used as a prove, the effects of stirring on each phase3 of an oscillation cycle in a batch BZ reaction strongly depend on the initial concentrations of the chemicals. Menzinger et al.4 suggested that the stirring effect in a batch BZ system is due to increasedoxygen transfer from the gaseous phase to the liquid phase. According to DAlba and Di Lorenzo,S the stirring effect in a batch BZ reaction is due to the exchange of oxygen and bromine molecules at the gas/liquid interface. Sevcik et a1.6 reported that the oscillation parameters depend on stirring even in a batch BZ system carried out in an oxygen-free atmosphere. In an experiment carried out in a continuously fed stirred tank reactor (CSTR), the concentrations of the reacting chemicals inside the reactor are maintained unchanged throughout the experiment by continuous feeding of the chemicals, and the oscillations generated are sustained in character. Also, very little contact between air and the solution inside the CSTR excludes the possibility that the oscillation parameters are affected at high stirring rate by the exchange of oxygen and bromine molecules at the gas/liquid interface. The effectiveness of mixing in a flow reactor is an important issue in chemical engineering dynamics because it determines the yield and distribution of the reaction products. There are two levels of mixing,' macromixing and micromixing. Macromixing is the formation of macroscopic heterogeneitiesand their breakdown into small segregated liquid parcels. This mixing process, not yet on the molecular level, is large enough with good stirring. Micromixing is the decay of the segregation by molecular diffusion and may have a characteristic time of the order of 1 s. The effects of stirring in the CSTR mode was investigated in the past mainly for two systems, the C102-/1and the Br03-/Ce(III)/Br reaction,10 the minimal bromate oscillator (MBO). The experimental observationloof stirring effect on MBO in a CSTR has been obtained in a computer simulation by Gyorgyi et al.11 using a phenomenological model of micromixing.'
* Address
correspondence to this author at Ghanarajpur (Jalapara) Dhaniakhali, Hooghly, WB 712302, India. Abstract published in Advance ACS Absfracrs, September 1, 1993.
The rate constants of the component reactionsof a BZ reaction should depend12 through the Arrhenius equation on the temperature at which the experiment is carried out. In the present work we have investigated a systematic study of stirring and temperature effects on the BZ reactionsin a CSTR using malonic (MA) and gallic acid (GA)13-15 as organicsubstrates. An attempt has been made to correlate the dynamical role of stirring and temperature as bifurcation parameters in Hopt bifurcation16 experiments.
Experimental Section The experimentswere carried out in a thermostated cylindrical CSTR (volume 21 -4mL) with appropriate concentrationsof the organic substrate and the other component chemicals of the BZ reaction. The stirrer blades (dimension 15 X 2 mm) were placed 14 mm above the bottom (diameter 30 mm) of the CSTR. A bright Pt electrode (dimension 7 X 4 X 0.5 mm) was set horizontally inside the reactor such that its tip lies just above the stirrer blades. The Pt electrode potentials were recorded on a x-t chart recorder with reference to a Hg-Hg2S04-Na2S04 electrode placed into the feed stream of sodium bromate solution before enteringinto the reactor. The chemicals from the reservoirs were fed into the CSTR by a multichannel peristaltic pump in a nonpremixed mode. The accuracy of the thermostat and the calibration of the stirring rate was within AO.1 OC and *OS% rpm, respectively. The experiments were conducted at different temperaturesand stirring rates for MA and GA organicsubstrates separately. The chemicals used were prepared from analytical grade reagents.
Results and Discussion Malonic Acid. The oscillation period and amplitude as a function of stirring rate are shown in parts a and b of Figure 1, respectively, at different temperatures. The plots of the maxima (V-) or the minima (Vdn)of theoscillation potentialsvs stirring rate are shown in Figure IC for the same different temperatures. The traces of oscillation potentials at three different temperatures (15, 25, and 35 "C)for S = 1500rpm are shown in Figure 2. The oscillation period and amplitude as a function of temperature at S = 1500 rpm are demonstrated in parts a and b of Figure 3, respectively. Figure l a and 3a show that the oscillation peroid increases sharply with decrease of temperature. Figure 3a obeys the emperical relation given below period = 2.7 e x p ( 4 0 9 X temperature) (1) Stirring has little effect on the oscillation period unless the temperature is very low and stirring very high. In general the
0022-3654/93/2097-10059$04.00/00 1993 American Chemical Society
loo60 The Journal of Physical Chemistry, Vol. 97, No. 39, 1993
Dutt and Muller
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I5 O C . The potential increases in the direction from top to bottom in each trace (for the absolute values of the potentials see also Figure IC); concentrations and residence time as described in Figure 1,
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Figure 3. Oscillation period and amplitude as a function of temperature for the MA sytem at S = 1500 rpm: (a, top) period, (b,bottom) amplitude.
Concentrations and residence time as described in Figure 1.
oscillation period has a tendency to decreaseslightly at high stirring rate, and this decrease is more pronounced at low temperature (15 "C) and very high stirring rate (>2500 rpm). This result seems opposite to that reported by previous workers2b9- in batch experimentsof the BZ reaction using MAas the organic substrate where the increase of stirring rate was found to increase the
oscillation period. Figure l b and 3b show that the oscillation amplitude decreases with increse of temperature and Figure 3b follows the following emperical equation
+
amplitude = -39 ln(temperature) 205 (2) At high temperature (35 "C), the amplitude increases slightly with increaseof stirring rate. But ina relatively low temperature range 15-25 'C stirring has little effect up to 2500 rpm and
The Journal of Physical Chemistry, Vol. 97, No. 39, 1993 10061
Belousov-Zhabotinskii Reaction
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50 sFigure 4. Potential traces at 25 'C (top) and 35 OC (bottom) for five different stirring rates with GA as the organic substrate: a, 3000; b, 2500,c,2OOO;d,1500,e, 1OOOrpm. Thepotentialincreasesinthedirtction from top to bottom in each trace (for the absolutevalues of the potentials see also Figure 5). The composition inside the CSTR: [NaBrO& = 0.25 M;[GA]o = 0.035 25 M;[Ferroin]~= 0.OOO 37 M;[H~S04]0= 1 M. Residence time = 38.9 min.
beyond that the stirring effect is highly irregulra. Figure IC demonstrates that due to increase of temperature from 15 to 35 OC the potential of the oxidizing (high potential) phase decreases about 3-fold compared to that of the reducing (low potential) phase in an oscillation cycle. Gallic Acid. The traces of oscillation potentials for four different stirring rates (3000, 2500, 2000, 1500, 1000 rpm) are shown in parts a and b of Figure 4 at two different temperatures, 25 and 35 OC, respectively. At 25 O C (Figure 4a), the low stirring oscillation traces are highly complex in nature and there are many small-amplitude oscillations of varying amplitudes between two large oscillations. The oscillationsbecome more and more regular as the stirring is increased. The plots of the maxima ( VmX)or the minima ( VmX)of the oscillation potentials vs stirring rate for GA system are shown in Figure 5 at three different temperatures. To determine the value of V , or Vd,,at low stirring rates, where both small and large amplitude oscillations exist, we considered only the oscillations of the largest amplitudes. After the
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Ngure 5. Potentials corresponding to the maxima (V,) or the minima ( V h )of the largest oscillation amplitudes as a function of stirring rate in the GA system at three different temperatures: 25,30, and 35 O C . The dotted lines for ,V and the solid lines containing the same symbols for the corresponding V h ;the maximum error is +5 mV in most of the oscillations; concentrations and residence time as described in figure 4 (see the text for more information about ,V and V& at low stirring rates). oscillations become regular at some higher stirring rate the oscillation period is found to decrease with increase of stirring rate. A recent experiment'sc on the GA system in a batch reactor reported that at high stirring rate the high-potential oxidizing phase continues for a longer time, resulting in the increase of oscillation period. It was also shown that at high stirring rates the maxima and the minima of the trace of electrochemical potential of Pt electrode were shifted to higher values. These observations were explained by assuming that at a higher stirring rate more bromine gas escapes at the surface of the solution by gas-air interchange. But in the present CSTR experiment we observed17 that at a high stirring rate the oscillation period is decreased and the oxidizing phase (high potential) continues for a shorter time at 25 "C (Figure 4a). But at high temperature (35 O C , Figure 4b) no significant effect on oscillation period is observed at high stirring rate. We also observed that the potentials of the maxima of the oscillations at different temperatures are not much different at low stirring rate, whereas the minima decrease more and more as the stirring rate is increased and the temperature decreased (Figure 5). In the present case there is very little contact between air and the surface of the solution inside the CSTR and the possibility of escape of bromine gas from solution to air at high stirring rate is almost ruled out. The stirring effect is expected to be determined solely by the macroand micromixing7processes, which is perhaps the reason that the observations of stirring effect between batch and CSTR experiments are so widely different. A comparison of parts a and b of Figure 4 (for the GA system) gives the following important observations. The oscillation amplitude decreases at high temperature and increases at high stirring rate. The temperature effect is very strong in this system, like that in the MA system. At 25 and 35 OC the amplitude of oscillation in the GA system increases by 77% and 160% respectively, when the stirring rate is increased by about 200%. This demonstrates that the stirring effect in the GA system is very large. Figure 5 shows that with the increase of temperature from 25 to 35 O C , the maxima of the oscillations (V-) decrease whereas the minima (Vd,,) increase about 3 4 times the decrease of the maxima to make the oscillation amplitude (V- - V ~ , ) smaller at high temperature. Hysteresis. The oscillations in the GA system for which a strong stirring effect has been reported in the preceeding section
Dutt and Miiller
10062 The Journal of Physical Chemistry, Vol. 97, No. 39, 1993 800 2
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Figure 6. Hysteresis between an oscillating branch and a flow branch in the GA system in terms of potential as a function of stirring rate at 25 O C . The vertical lines with circles at the ends indicate oscillation amplitudesat different stirring rates: open circles,when stirringincreased and closed, when decreased after an up transition from the flow branch to theoscillatory branch. Thecomposition inside theCSTR [NaBrOJo = 0.2 M;[GA]o = 0.0345 M;[ferroin[o = O.OO0 37 M;[ H ~ S O &=J 1 M;residence time = 31.9 min. 750
1 Thermodynamic Branch
1 Down
The results reported above indicate that temperature and stirring have a significant dynamical role in controlling the oscillationamplitude and the bistable behavior in the GA system. This dependence of oscillation amplitude on stirring and temperature is exponential in character. Therefore the temperature and stirring are secondarybifurcation parameters in a supercritical HopfI6 bifurcation experiment, while the primary bifurcation parameters are the concentrations of the chemicals. The temperature effect on the oscillationamplitude and period of both BZ systems reported here are qualitatively similar; high temperature decreases amplitude and period in both cases. But it is important to note that, while stirring has a large effect on the GA system (viz., complex oscillation at low stirring and big amplitude at high stirring), no significant dependence on stirring is observed in the MA system. For the GA system the experiment was carried out at an arbitrary combination of concentration of the chemicals, which produces oscillations in a CSTR mode. The concentration of gallic acid in the reservoir could not be increased further due to its upper solubility limit and presently we have no idea about the phase diagram of this system in concentration space. We have not checked the stirring effect on the MA system further with different ratios of bromate and malonif acid concentrations. However, wedo not rule out the possibility that, at suitable concentrationZbof the chemicals, the MA system may also exhibit a strong stirring effect. It seemsthat a computer simulationusing the phenomenological model of micromixing7J1is a plausible way to explain the stirring effect in both BZ systems in the CSTR mode. The information excepting the organic part of the reaction is now available for the computer simulation of the stirring effect in the MA system. But problems should arise in the case of the GA system because very little is known about its mechanism. The computer simulation of the temperature effect is very much uncertain in both systems either because the activation energies of some mechanistic steps are unknown in the literature (e.g., for the MA system) or the mechanisn itself (e.g., for the GA system) has not been established as yet. Also the fact that the GA system without ferroin can undergo batch oscillation and it is absolutely necessary to explore the uncatalyzed GA system in a CSTR for understanding of the dynamical behavior of the uncatalyzed part of the present GA system and in general the uncatalyzed class of bromate oscillators. In a recent experimental investigationin CSTR, we have obtained a concentration regime in the uncatalyzed GA system where a bistability between an oscillatory branch and a flow branch exists in [BrO&--[Br]o- concentration space. We hope to report it in a subsequent paper.
350 Flow Branch
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Figure 7. Hysteresis between a thermodynamic branch (high potential) and a flow branch (low potential) in the GA system in terms of potential as a function of stirring rate at 15 OC. Up and down transitions are observed at very low and high stirring rate. The concentrations and residence time as described in Figure 6.
are those when the system resides on a high potential oscillatory branch and exhibits a bistability with a low potential flow branch in terms of potential as a function of stirring rate as shown in Figure 6. The system starts oscillation at low stirring rate and the oscillation amplitude increases as the stirring is increased until it transits (down transition) to a low-potential flow branch at high stirring rate. The up transition from flow to oscillatory branch takes place at low stirring rate, which can be achieved by decreasing the stirring rate in small steps. The normal bistability between a thermodynamic (high potential) branch and a flow (low potential) branch in the same system is observed at low temperature (15 "C) as shown in Figure 7 in terms of potential as a function of stirring rate. In this case also the up and the down transitions take place at very low and very high stirring rates, like those in Figure 6.
Acknowledgment. We acknowledge technical assistance from W. Riiller and H. Schliiter. References and Notes (1) Epstein, I. R. Narure 1990, 346, 16. (2) (a) Ruoff, P.; Noyes, R. M. J . Phys. Chem. 1989, 93, 7394. (b) Lopez-Thomas, L.;Saguts, F. J . Phys. Chem. 1991,95, 701. (3) Field, R. J.; Koros, E.; Noyes, R. M. J. Am. Chem. Soc. 1972, 94, 8649. (4) Menzinger, M.; Jankowski, P. J . Phys. Chem. 1986, 90,1217. ( 5 ) D'Alba, F.; Di Lorcnzo, S . J . Chem. Soc.;Faraday Trans. 1983,179, 39. (6) Sevcik, P.; Adamcikova, L. Chem. Phys. k t r . 1988, 146, 419; J . Chem. Phys. 1990, 91, 1012. (7) (a) Nauman, E. B.; Buffham, E. A. Mixing in Continuous Flow Systems; Wiley: New York, 1983. (b) Wtsterp, K. R.; Van Swaaij, W. P. M.; Beenackkers, A. A. C. Chemical Reactor Design and Operation; Wiley: New York, 1983. (c) Villermaux, J . ACS Symp. Ser. 1983, 226, 135. (d)
Villermaux, J. In Encyclopedia of Fluid Mechanics; Chereminisinoff,N. P.; Ed.; Gulf Publishing: Houston, 1986; Chapter 27. (8) (a) Menzinger, M.; Dutt, A. K.J . Phys. Chem. 1990,944510. (b) Ochiai. E. I.: Menzinger. M. J . Phvs. Chem. 1990. 94. 8866. (9) (a) Roux, J.-E.;'Dc~cppe;, P.;Boissonade, J.'Phys. h i t . A 1983, 97, 168. (b) Luo, Y.; Epstein, I. R. J . Chem. Phys. 1986, 85, 5733. (c) Menzinger, M.; Boukalouch, M.; De Kepper, P.; Boissonade, J.; Roux, J.-C.;
Belousov-Zhabotinskii Reaction Saadoui, H.J. Phys. Chcm. 1986,90,313. (d) Menzinger, M.; Giraudi, A. J . Phys.Chcm. 1981,91,4391. (e) BouLalouch,M.;Boissonade,J.;DeKeppcr, P. J. Chim. Phys. 1987,84, 1353. (IO) (a) Dutt, A. K.; Menzinger, M. J. Phys. Chcm. 1990,944867. (b) Dutt, A. K.; Menzinger, M.J. Phys. Chem. 1991, 95, 3429. ( 1 1 ) Gyoergyi, L.; Field, R. J. J. Phys. Chcm. 1992, 96, 1220. (12) Kumpinsky, E.; Epstein, I. R. J. Phys. Chcm., 1985, 89, 688. (13) Babu, J. S.;Srinivaaulu, K. Proc. Indian Natl. Sci. Acad. (India) 1976,42A, 361;Bull. Chem.Soc. Jpn. 1976,49,2875;1.Chem.Soc., Faraday Trans I1977, 73, 1843.
The Journal of Physical Chemistry, Vol. 97, No. 39, I993 10063 (14) Koros, E.; Orban, M. Nature 1978, 273, 371. E.F. J. Phys. C h " 1989,93,2388. (b) Dutt, A. K.; Banerjee, R. S. Chcm. Phys. Lett. 1983, 99, 186. (c) Dutt, A. K.; Menzinger, M. J . Phys. Chcm. 1992,96,8441. (16) Guckenheimer, J.; Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Buurcations of Vector Fields; Springer Verlag: New York 1986; Chapter 3. (17) The small oscillations at the bottom of the big oscillations for S = 2500, 3000 rpm (see Figure 4a) are pcrhap the evidence of strong heterogeneitiw present wen at high stirring rates. (15) (a) Jwo, J. J.;Chang,
